Square wave (waveform)

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Antiderivative

Triangle wave

Codomain

{ − 1 , 1 } {\displaystyle \left\{-1,1\right\}}

Domain

R ∖ { n 2 } , n ∈ Z {\displaystyle \mathbb {R} \setminus \left\{{\tfrac {n}{2}}\right\},n\in \mathbb {Z} }

Fields of application

Electronics, synthesizers

Fourier series

x ( t ) = 4 π ∑ k = 1 ∞ 1 2 k − 1 sin ⁡ ( 2 π ( 2 k − 1 ) t ) {\displaystyle x(t)={\frac {4}{\pi }}\sum _{k=1}^{\infty }{\frac {1}{2k-1}}\sin \left(2\pi \left(2k-1\right)t\right)}

General definition

x ( t ) = 4 ⌊ t ⌋ − 2 ⌊ 2 t ⌋ + 1 , 2 t ∉ Z {\displaystyle x(t)=4\left\lfloor t\right\rfloor -2\left\lfloor 2t\right\rfloor +1,2t\notin \mathbb {Z} }